论文标题
量子Lifshitz模型中激发态的纠缠熵
Entanglement Entropy of Excited States in the Quantum Lifshitz Model
论文作者
论文摘要
在这项工作中，我们计算了量子Lifshitz模型的某些激发态的纠缠熵。量子LIFSHITZ模型是一个2 + 1维的玻色量量子场理论，其空间和时间之间的各向异性缩放比例对称性属于量子二聚体模型的通用类别及其概括。我们考虑的状态是通过在模型的空间歧管上激发拉普拉斯 - 贝特拉米操作员的特征模式来构建的。我们执行复制品计算，并发现每当满足简单的假设时，都可以通过分析来评估任何此类激发状态的双分部分纠缠熵。我们表明，对于矩形上的所有激发态和球体上的几乎所有激发态，都可以满足该假设，并在两个几何形状中提供明确的例子。我们发现，激发的状态纠缠熵遵守了一项区域法，并与两个通用常数有关地面状态的纠缠熵有关。当将所有激励放在同一本本本元上时，我们观察到对激发数的对数依赖性。
In this work we calculate the entanglement entropy of certain excited states of the quantum Lifshitz model. The quantum Lifshitz model is a 2 + 1-dimensional bosonic quantum field theory with an anisotropic scaling symmetry between space and time that belongs to the universality class of the quantum dimer model and its generalizations. The states we consider are constructed by exciting the eigenmodes of the Laplace-Beltrami operator on the spatial manifold of the model. We perform a replica calculation and find that, whenever a simple assumption is satisfied, the bipartite entanglement entropy of any such excited state can be evaluated analytically. We show that the assumption is satisfied for all excited states on the rectangle and for almost all excited states on the sphere and provide explicit examples in both geometries. We find that the excited state entanglement entropy obeys an area law and is related to the entanglement entropy of the ground state by two universal constants. We observe a logarithmic dependence on the excitation number when all excitations are put onto the same eigenmode.
